Wireless connection to D500 is not supported by Helicon Remote, and possibly never will be due to the way this camera works. Note that D500 not and never was on the list of cameras that Helicon Remote supports wirelessly (http://www.heliconsoft.com/supported-cameras/ , bottom of the page).
I used to think D500 should work but now I realize I was wrong - apologies for the misleading previous replies on this matter.

Stas, You don't say what it is about the D500 that is different to make it incompatible, so do think that the D500 is an "oddball" in this respect or do think that the incompatibilities with Remote are going to be a trend with more new Nikon cameras?

That mistake has been corrected over a year ago and was only present on our website for a short time. The information on our website right now is correct: D5600 is fully supported with USB connection, but wireless connection is not supported (it's not listed under Wi-Fi cameras).

I will be more than happy to be proven wrong, but I spent several hours yesterday trying without result. I am using it with the Nikon D5600 camera (which is listed as fully compatible for USB as you stated), and a Samsung GT-S7582L smartphone with Android 4.2.2 (which is also listed as compatible). This is a Snapbridge camera, so I did not even try to connect it wirelessly. I have the correct original USB cable and an adapter (USB OTG) which have both been tested and work. I have tried it with the phone>USB as both a media device (MTP) and camera (PTP), and with USB debugging activated. So what am I doing wrong?

Most likely, there's a problem with OTG support in your Android. Please follow the guide we have specifically written for this very issue, it will help you figure out exactly where the problem is and whether or not it can be solved: https://www.heliconsoft.com/faq-helicon-remote/#camera_not_detected

Your are absolutely right and I have been proven wrong. I contacted Samsung and they responded that while Android 4.2.2 has no problem with OTG support, the model phone that I use (GT-S7582L-Galaxy Duo) does not support OTG and there is no retrofit available. If you can, please include this alert on your compatibility list. I guess I will have to look for another solution, because Nikon Snapbridge is also not compatible with this phone. What a pain.